- Tytuł:
- Arc Fault Tolerance of Cartesian Product of Regular Digraphs on Super-Restricted Arc-Connectivity
- Autorzy:
-
Zhang, Guozhen
Wang, Shiying - Powiązania:
- https://bibliotekanauki.pl/articles/31343704.pdf
- Data publikacji:
- 2019-02-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
fault tolerance
restricted arc-connectivity
super-restricted arc- connectivity
Cartesian product
regular digraph - Opis:
- Let $ D = (V (D),A(D)) $ be a strongly connected digraph. An arc set $ S \subseteq A(D) $ is a restricted arc-cut of $D$ if $ D − S$ has a non-trivial strong component $ D_1 $ such that $ D − V (D_1)$ contains an arc. The restricted arc-connectivity $ \lambda^‘(D) $ is the minimum cardinality over all restricted arc-cuts of $D$. In [C. Balbuena, P. García-Vázquez, A. Hansberg and L.P. Montejano, On the super-restricted arc-connectivity of s-geodetic digraphs, Networks 61 (2013) 20-28], Balbuena et al. introduced the concept of super-$ \lambda^' $ digraphs. In this paper, we first introduce the concept of the arc fault tolerance of a digraph $D$ on the super-$ \lambda^‘ $ property. We define a super-$ \lambda^′ $ digraph $D$ to be $m$-super-$ \lambda^‘ $ if $D − S $ is still super-$ \lambda^‘ $ for any $ S \subseteq A(D) $ with $ |S| \le m $. The maximum value of such $m$, denoted by $S_{ \lambda^’ } (D) $, is said to be the arc fault tolerance of $D$ on the super-$ \lambda^‘$ property. $ S_{ \lambda^’ } (D) $ is an index to measure the reliability of networks. Next we provide a necessary and sufficient condition for the Cartesian product of regular digraphs to be super-$ \lambda^‘ $. Finally, we give the lower and upper bounds on $ S_{ \lambda^’ } (D) $ for the Cartesian product $D$ of regular digraphs and give an example to show that the lower and upper bounds are best possible. In particular, the exact value of $ S_{ \lambda^’ } (D) $ is obtained in special cases.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2019, 39, 1; 95-116
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł